Analytical model for information flow propagation wave under an information relay control strategy in a congested vehicle-to-vehicle communication environment

Vehicular traffic congestion in a vehicle-to-vehicle (V2V) communication environment can lead to congestion effects for information flow propagation. Such congestion effects can impact whether a specific information packet of interest can reach a desired location, and if so, in a timely manner to influence the traffic system performance. Motivated by the usefulness and timeliness of information propagation, this paper aims to characterize the information flow propagation wave (IFPW) for an information packet in a congested V2V communication environment under an information relay control strategy. This strategy seeks to exclude information that is dated in the communication buffer under a first-in, first-out queue discipline, from being relayed if the information flow regime is congested. It trades off the need to enable the dissemination of every information packet as far as possible, against the congestion effects that accrue because of the presence of multiple information packets. A macroscopic two-layer model is proposed to characterize the IFPW. The upper layer is formulated as integro-differential equations to characterize the information dissemination in space and time under this control strategy. The lower layer adopts the Lighthill-Whitham-Richards model to capture the traffic flow dynamics. Based on the upper layer model, a necessary condition is derived which quantifies the expected time length that needs to be reserved for broadcasting the information packet of interest so as to ensure the formation of an IFPW under a given density of V2V-equipped vehicles. When the necessary condition is satisfied under homogeneous conditions, it is shown that the information packet can be propagated at an asymptotic speed whose value can be derived analytically. Besides, under the proposed control strategy, only a proportion of vehicles (labeled asymptotic density of informed vehicles) can receive the specific information packet, which can be estimated by solving a nonlinear equation. The asymptotic IFPW speed, the asymptotic density of informed vehicles, and the necessary condition for the IFPW, help in evaluating the timeliness of information propagation and the influence of traffic dynamics on information propagation. In addition, the proposed model can be used to numerically estimate the IFPW speed for heterogeneous conditions, which can aid in the design of traffic management strategies built upon the timely propagation of information through V2V communication.